What is 16y^2-9x^2+36x+96y-36=0 ?

The solution to 16y^2-9x^2+36x+96y-36=0 is Hyperbola with (h,k)=(2,-3),a=3,b=4

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16y^2-9x^2+36x+96y-36=0

16 y^{2} - 9 x^{2} + 36 x + 96 y - 36 = 0

(h, k) = (2, - 3), a = 3, b = 4

Solution steps

16 y^{2} - 9 x^{2} + 36 x + 96 y - 36 = 0

Rewrite

16 y^{2} - 9 x^{2} + 36 x + 96 y - 36 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 3 ) ) ^{2}}{3 ^{2}} - \frac{( x - 2 ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, - 3), a = 3, b = 4

4 x^{2} - 25 y^{2} - 8 x - 100 y - 196 = 0

- \frac{x ^{2}}{25} + \frac{y ^{2}}{144} = 1

y^{2} - 2 x^{2} - 4 = 0

9 x^{2} - 16 y^{2} - 18 x + 32 y - 151 = 0

\frac{( y + 3 ) ^{2}}{4} - \frac{( x - 2 ) ^{2}}{9} = 1

What is 16y^2-9x^2+36x+96y-36=0 ?
The solution to 16y^2-9x^2+36x+96y-36=0 is Hyperbola with (h,k)=(2,-3),a=3,b=4